If the Ethiopians got nothing about their new year from the Copts then why do you both happen to have the same day for the new year on your respective calendars?
It would be easy to ask him, How the difference in year came/the coptic 1727 and the Ethiopian 2003/?
Coming to my justifications,
New year occurs on the day on which the rainy season is wind up, and the bright autumn sunlight shines, after a 5 day month,
Each month has 30 days, we have 12 months with 30 days, and one month 5 /6 days in each 4th year/.
In the book of Enoch it says "When the sun rises in heaven, it goes forth through this fourth gate thirty days, and by the fourth gate in the west of heaven on a level with it descends."Chapter 71:17 --- Seasons are gates, and each month bear 30 days....and goes on.
Please read the whole Chapter 81, to know how system is working in the following link http://reluctant-messenger.com/1enoch61-105.htm
In Ethiopian Orthodox Church bible its arranged that way, anyways.
It may be Nile which links the two countries which made seasonal similarity.
But after Christianity came into stage, new calculations needed to fix the Special dates into the existing calendar.
That is why the Egyptian Demetrius' mathematics was used.